Principles of Microeconomics / Unit 5 MIC 0407 worked example, 60 to 90 seconds
Finding the Best Bundle
The idea
With two goods, a budget and each good's marginal utility at every quantity, find the best bundle by spending the budget one purchase at a time. Compute marginal utility per dollar for the next unit of each good. Buy the one with the higher number. Recompute and repeat until the budget is gone. At the finish, the two goods' marginal utility per dollar should match or nearly match, and any switch of a dollar between them should lower total utility.
In practice
Worked example: a budget of twelve dollars, sandwiches at four dollars with marginal utilities of forty, thirty-two, twenty and twelve, and juices at two dollars with marginal utilities of sixteen, twelve, eight and four. Per dollar, the first sandwich gives ten and the first juice eight: buy the sandwich. Next, the second sandwich gives eight and the first juice eight: buy both, spending ten so far. The third sandwich gives five and the second juice six: buy the juice, reaching twelve dollars. The bundle is two sandwiches and two juices, and the last purchases gave eight and six per dollar, the closest match the budget allows.
Where people slip
Two cautions. Lumpy goods rarely equalize the ratios exactly; the rule is met as closely as whole units permit, and a switch that overshoots lowers utility. And a bundle that leaves money unspent is never best while any marginal utility is positive.
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